CN104574319B - The blood vessel Enhancement Method and system of a kind of lung CT image - Google Patents
The blood vessel Enhancement Method and system of a kind of lung CT image Download PDFInfo
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- 210000004204 blood vessel Anatomy 0.000 title claims abstract description 55
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Abstract
The invention belongs to image processing field, there is provided the blood vessel Enhancement Method and system of a kind of lung CT image.This method and system are that Vessel Enhancing Diffusion (VED) algorithm is improved, estimating after every bit belongs to the possibility of tubular structure, pass through rod Tensor Voting, characteristic point and characteristic vector are reconstructed, recycle spread function to carry out image enhaucament afterwards.Relative to VED algorithms, due to make use of the tensor direction of neighborhood, blood vessel trend to vascular wall has carried out rod Tensor Voting, so as to correct for the tensor direction around vascular wall and be reconstructed new tensor direction, diffusion of the blood vessel intensity along blood vessel tangent plane can be preferably reduced using the tensor direction of reconstruct, diffusion of the enhancing along vessel directions simultaneously, reach suppression noise, strengthen the effect of blood vessel feature, solve the presence of VED algorithms tubular structure edge feature direction it is mixed and disorderly caused by enhancing effect distortion the problem of.
Description
Technical Field
The invention belongs to the field of image processing, and particularly relates to a blood vessel enhancement method and system for a lung CT image.
Background
The CT image is a scanned image of a part of a human body, can image tissues such as blood vessels, tumors and the like, and assists a doctor in timely selecting a reasonable treatment method. For a lung CT image, due to the presence of a large amount of tissue with tubular structures (e.g. bronchi, blood vessels, etc.), in order to highlight these tubular structures, suppress background noise, and aid in the diagnosis of lung diseases, it is necessary to enhance them by image enhancement techniques.
The prior art proposes a variety of methods for vascular enhancement of lung CT images. Among them, multiscale vessel enhancement algorithms based on Hessian (Hessian) matrix are a common method. The method distinguishes blood vessels from the background by using the eigenvalues and eigenvectors of the Hessian matrix and extracts local geometric characteristics by using a second derivative. In all multiscale vessel enhancement algorithms based on the Hessian matrix, the Frangi algorithm considers all characteristic values and makes geometric explanation for vessel detection, and the method can detect most vessels under different scales and is quite widely applied. However, the Frangi algorithm is sensitive to noise, and a large amount of scattered noise appears after enhancement, and in addition, the algorithm only responds to a linear structure and has an inhibiting effect on other structures, for example, a small response can be obtained at a blood vessel intersection, so that a blood vessel fracture phenomenon is caused.
The Vessel Enhanced Diffusion (VED) algorithm improves the Frangi algorithm in two ways. Firstly, the VED algorithm adds a smoothing factor in a vessel function of the Frangi algorithm, so that the influence on noise can be reduced, and the vessel function becomes smooth and continuous; and secondly, the VED algorithm diffuses the detected tubular structure, so that the defect that the blood vessel is broken as detected by the Frangi algorithm is overcome.
However, although the VED algorithm solves the problem of noise and fracture of the Frangi algorithm to a certain extent, due to the existence of noise, the diffusion direction of the blood vessel wall is not consistent with the direction of the blood vessel as the middle part of the blood vessel, but is interfered by surrounding noise, and a phenomenon of disordered diffusion directions occurs, and the disordered diffusion directions cause the blood vessel to possibly diffuse towards the direction of the section of the blood vessel, so that the diffused blood vessel is thicker than the original blood vessel, and the effect of blood vessel enhancement is distorted.
Disclosure of Invention
The invention aims to provide a blood vessel enhancement method of a lung CT image, and aims to solve the problem that the diffusion direction of a VED algorithm at a blood vessel wall is disordered due to the existence of noise, so that the blood vessel enhancement effect is distorted.
The invention is realized in such a way that a blood vessel enhancement method of a lung CT image comprises the following steps:
calculating a Hessian matrix of each point in the image, and a characteristic value and a characteristic vector of the Hessian matrix, and estimating the possibility that each point belongs to a tubular structure according to the characteristic value and the characteristic vector;
taking the minimum direction of the eigenvalue of the point with the probability greater than 0 as the normal direction, carrying out rod tensor voting on other points with the probability greater than 0 in the neighborhood, and reconstructing the eigenvalue and eigenvector of each point with the probability greater than 0 according to the voting result to determine the trend direction of the tubular structure of each point with the probability greater than 0;
and updating the intensity of each point with the probability being greater than 0 in the image by using a diffusion function according to the reconstructed feature vector until the updating times reach the maximum iteration times.
It is another object of the present invention to provide a vessel enhancement system for pulmonary CT images, the system comprising:
the calculation module is used for calculating a Hessian matrix of each point in the image, the eigenvalue and the eigenvector of the Hessian matrix, and estimating the possibility that each point belongs to the tubular structure according to the eigenvalue and the eigenvector;
the reconstruction module is used for carrying out the rod tensor voting on other points with the possibility of being greater than 0 by taking the characteristic value minimum direction of the point with the possibility of being greater than 0 as the normal direction, and reconstructing the characteristic value and the characteristic vector of each point with the possibility of being greater than 0 according to the voting result so as to determine the trend direction of the tubular structure of the point with the possibility of being greater than 0;
and the diffusion module is used for updating the intensity of each point with the possibility of being greater than 0 in the image by using a diffusion function according to the reconstructed feature vector until the updating times reach the maximum iteration times.
The vascular enhancement method and the vascular enhancement system for the lung CT image, which are provided by the invention, improve the VED algorithm, reconstruct the eigenvalue and the eigenvector by rod tensor voting after estimating the possibility that each point belongs to a tubular structure, and then enhance the image by using a diffusion function. Compared with the VED algorithm, the tensor direction of the neighborhood is utilized, and the bar tensor voting is carried out on the blood vessel trend of the blood vessel wall, so that the tensor direction around the blood vessel wall is corrected, a new tensor direction is reconstructed, the diffusion of the blood vessel strength along the blood vessel tangent plane can be well reduced by utilizing the reconstructed tensor direction, the diffusion along the blood vessel direction is enhanced, the noise is suppressed, the effect of blood vessel characteristics is enhanced, and the problem of enhancement effect distortion caused by disorder of the edge characteristic direction of the tubular structure in the VED algorithm is solved.
Drawings
FIG. 1 is a flowchart of a method for enhancing blood vessels in a pulmonary CT image according to an embodiment of the present invention;
FIG. 2 is a detailed flow chart of the method for obtaining the probability that each point belongs to a tubular structure according to the embodiment of the present invention;
FIG. 3 is a detailed flowchart of reconstructing eigenvalues and eigenvectors in an embodiment of the present invention;
FIG. 4 is a block diagram of a vessel enhancement system for CT images of the lungs according to an embodiment of the present invention;
FIG. 5 is a block diagram of the calculation module of FIG. 4;
fig. 6 is a block diagram of the reconstruction module of fig. 4.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In order to solve the phenomenon that a VED algorithm is influenced by noise and diffusion disorder appears on a blood vessel wall, the blood vessel enhancement method and the blood vessel enhancement system of the lung CT image provided by the invention improve the VED algorithm, after the possibility that each point belongs to a tubular structure is estimated, eigenvalues and eigenvectors are reconstructed by rod tensor voting, and then, image enhancement is carried out by using a diffusion function.
Fig. 1 shows a flow of a blood vessel enhancement method for a pulmonary CT image provided by an embodiment of the present invention, which includes the following steps:
s1: and calculating the Hessian matrix of each point in the image, the eigenvalue and the eigenvector of the Hessian matrix, and estimating the possibility that each point belongs to the tubular structure according to the eigenvalue and the eigenvector.
Further, as shown in fig. 2, step S1 may further include the following steps:
s11: and smoothing the image by utilizing a multi-scale Gaussian function.
Assuming that G (x, y, z; sigma) is a three-dimensional Gaussian function with the scale sigma, the image I (x, y, z) is smoothed to obtain a result I under the scale sigmaσ(x, y, z) is represented by:wherein,
s12: and under each scale, calculating the Hessian matrix of each point in the image according to the smoothing result.
Assuming that at the scale σ, the Hessian matrix at the point (x, y, z) in the image is Hσ(x, y, z), then it is expressed as:
s13: and carrying out eigenvalue decomposition on the Hessian matrix of each point to obtain three eigenvalues and eigenvectors corresponding to the three eigenvalues one by one respectively.
In the embodiment of the invention, for Hessian matrix HσThe three eigenvalues obtained after decomposition of (x, y, z) are recorded as λ1、λ2、λ3And satisfy | λ1|≤|λ2|≤|λ3L, |; the three eigenvectors corresponding to the three eigenvalues one by one are recorded as
Eigenvalues and eigenvectors of the Hessian matrix may describe the geometric characteristics of the tubular structure. Specifically, for a point belonging to the tubular structure, the feature value corresponding to the feature vector of the point along the trend of the blood vessel is the smaller one of the three feature values; the other two eigenvectors along the tangent plane direction perpendicular to the blood vessel trend are stretched into a plane, the eigenvalues corresponding to the other two eigenvectors are close in size and are the larger two of the three eigenvalues, namely, the condition of | lambda is satisfied3|≈|λ2|＞＞|λ1|≈0。
S14: from the eigenvalues and eigenvectors of each point, the likelihood that the corresponding point belongs to a tubular structure at each scale is estimated.
Assuming that under the scale sigma, three characteristic values corresponding to points (x, y, z) in the image satisfy lambda1|≤|λ2|≤|λ3The probability that a point (x, y, z) belongs to a tubular structure is Vs(σ), then:
wherein,coeff is a constant, α is a constant and 0 < α < 1, typically 0.5, β is a constant and 0 < β < 1, typically 0.5, and γ is a set constant.
S15: taking the maximum value of the possibility of each point under different scales as the final value of the possibility that the corresponding point belongs to the tubular structure.
Assuming that the final value of this probability is denoted as V, then:wherein σmin，σmaxRespectively, a minimum scale and a maximum scale.
S2: and (3) performing rod tensor voting on other points with the probability greater than 0 in the neighborhood by taking the characteristic value minimum direction of the point with the probability greater than 0 as a normal direction, and reconstructing the characteristic value and the characteristic vector of each point with the probability greater than 0 according to the voting result to determine the trend direction of the tubular structure of the point with the probability greater than 0.
Further, as shown in fig. 3, step S2 may further include the following steps:
s21: and (3) performing the vote tensor voting by taking the point with the probability greater than 0 as a voting point, taking the direction with the minimum eigenvalue of the corresponding voting point as a normal direction and taking other points with the probability greater than 0 in the neighborhood as vote number receiving points.
Suppose that three eigenvalues corresponding to points (x, y, z) with a probability greater than 0 satisfy | λ1|≤|λ2|≤|λ3I, the feature vector isThe rod tensor is S, the plate tensor is P, and the sphere tensor is B, then the Hessian matrix of the point (x, y, z) at the corresponding scale is H which can be decomposed into the sum of the rod tensor, the plate tensor and the sphere tensor, that is to say, there are: h ═ λ3-λ2)S+(λ2-λ1)P+λ1B, wherein the content of the compound B, (λ3-λ2) Indicating curved surface representation.
In the embodiment of the present invention, assuming that a point (x, y, z) having a probability greater than 0 is a voting point, a direction in which a feature value of the point (x, y, z) is minimum is taken as a voting pointAnd (3) voting other points R with the probability greater than 0 in the neighborhood in the normal direction, wherein R is a vote number receiving point, the number of votes cast from the point (x, y, z) to the point R is a wand tensor Stick (l, theta, phi) containing the direction and the intensity, and the conditions are as follows:
wherein,is a significant attenuation function, andtheta is the line l connecting point (x, y, z) and point RThe included angle of the plane formed by stretching the material,normal direction of the plane spanned iss is the arc length of the connecting line l, sigma designates the voting scale range and determines the size of the voting window, and c is a function of the scale range sigma, is used for restricting the curvature degradation degree and meets the following requirements:
in the embodiment of the invention, the characteristic vector corresponding to the minimum characteristic value is taken as the normal direction, and the significance of a rod tensor (lambda is added3-λ2) As weights, a vote tensor vote is performed. After the voting is finished, the voting accumulation of other points in the surrounding neighborhood is obtained for each probability in the image which is greater than 0.
S22: and reconstructing the characteristic value and the characteristic vector of each point with the probability greater than 0 according to the voting result to determine the trend direction of the tubular structure of each point with the probability greater than 0.
In the embodiment of the invention, the ticket numbers Stick (l, theta, pi) received at the ticket number receiving point R are accumulated, the accumulation process comprises the accumulation of tensor size and direction and the recording of T'R(x, y, z) is the accumulated tensor received by the receiving point, and the characteristic decomposition is carried out on the accumulated tensor:
wherein lambda'3|≤|λ′2|≤|λ′1L is T'RCharacteristic values of (x, y, z),is accumulated tensor T 'after voting is finished'R(x, y, z) corresponding to the minimum, next minimum and maximum eigenvalues of the eigenvalue, respectively, the direction of the eigenvector obtained at this timeI.e. the direction of correction of the original diffusion direction.
S3: and updating the intensity of each point with the probability greater than 0 in the image by using the diffusion function according to the reconstructed feature vector until the updating times reach the maximum iteration times.
In the embodiment of the invention, the VED algorithm is used for diffusing the possibility of the tubular structure in the graph, and the diffusion function is expressed as:wherein, VtIs the intensity of the vessel after diffusion, t is the diffusion time,is a divergence operator, D is a diffusion tensor, and satisfies:
wherein,the reconstructed feature vector, i.e., tensor T 'accumulated after the end of voting in step S22'RThe eigenvector of (x, y, z), ω being a parameter indicating the strength of the anisotropic diffusion, ω being 5, being a parameter ensuring that the diffusion tensor D is a positive definite matrix, L being 0.01, L being a parameter controlling the sensitivity of the diffusion function to the influence of the blood vessel, L being 2.
Fig. 4 shows the structure of the blood vessel enhancement system for lung CT images provided by the embodiment of the present invention, and for convenience of illustration, only the parts related to the embodiment of the present invention are shown, and the system may be a hardware unit, a software unit or a combination of hardware and software units built in other various image transformation systems.
Specifically, the blood vessel enhancement system for a lung CT image provided by the embodiment of the present invention includes: the calculation module 1 is used for calculating a Hessian matrix of each point in the image, and the eigenvalue and the eigenvector of the Hessian matrix, and estimating the possibility that each point belongs to the tubular structure according to the eigenvalue and the eigenvector; the reconstruction module 2 is used for performing rod tensor voting on the points with the probability greater than 0 in the neighborhood by taking the characteristic value minimum direction of the points with the probability greater than 0 as a normal direction, and reconstructing the characteristic value and the characteristic vector of each point with the probability greater than 0 according to the voting result to determine the trend direction of the tubular structure of each point with the probability greater than 0; and the diffusion module 3 is used for updating the intensity of each point with the possibility of being greater than 0 in the image by using a diffusion function according to the reconstructed feature vector until the updating times reach the maximum iteration times.
Further, as shown in fig. 5, the calculation module 1 may include: the smoothing submodule 11 is configured to smooth the image by using a multi-scale gaussian function; the first calculation submodule 12 is configured to calculate a Hessian matrix of each point in the image according to the smoothing result in each scale; the second calculation submodule 13 is configured to perform eigenvalue decomposition on the Hessian matrix of each point to obtain three eigenvalues and eigenvectors corresponding to the three eigenvalues one by one; an estimation submodule 14 for estimating, based on the eigenvalue and eigenvector of each point, the likelihood that each point belongs to a tubular structure at each scale; and the value sub-module 15 is used for taking the maximum value of the possibility of each point under different scales as the final value of the possibility that each point belongs to the tubular structure. The detailed execution flow of each sub-module corresponds to the steps S11 to S15, which are not repeated herein.
Further, as shown in fig. 6, the reconstruction module 2 may include: the voting submodule 21 is used for carrying out the rod tensor voting by taking each point with the probability greater than 0 as a voting point and taking other points with the probability greater than 0 as vote number receiving points; and the reconstruction submodule 22 is used for reconstructing the eigenvalue and the eigenvector of the accumulated tensor received by each point with the probability greater than 0 according to the voting result so as to determine the trend direction of the tubular structure of each point with the probability greater than 0. The detailed execution flow of each sub-module corresponds to the steps S21 to S22, which are not repeated herein.
In summary, the blood vessel enhancement method and system for lung CT images provided by the embodiments of the present invention improve the VED algorithm, and after the possibility that each point belongs to a tubular structure is estimated, eigenvalues and eigenvectors are reconstructed by rod tensor voting, and then image enhancement is performed by using a diffusion function. Compared with the VED algorithm, the tensor direction of the neighborhood is utilized, and the bar tensor voting is carried out on the blood vessel trend of the blood vessel wall, so that the tensor direction around the blood vessel wall is corrected, a new tensor direction is reconstructed, the diffusion of the blood vessel strength along the blood vessel tangent plane can be well reduced by utilizing the reconstructed tensor direction, the diffusion along the blood vessel direction is enhanced, the noise is suppressed, the effect of blood vessel characteristics is enhanced, and the problem of enhancement effect distortion caused by disorder of the edge characteristic direction of the tubular structure in the VED algorithm is solved.
It will be understood by those skilled in the art that all or part of the steps in the method for implementing the above embodiments may be implemented by controlling the relevant hardware through a program, and the program may be stored in a computer readable storage medium, such as ROM/RAM, magnetic disk, optical disk, etc.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (7)
1. A method for enhancing blood vessels of a lung CT image, the method comprising the steps of:
calculating a Hessian matrix of each point in the image, and a characteristic value and a characteristic vector of the Hessian matrix, and estimating the possibility that each point belongs to a tubular structure according to the characteristic value and the characteristic vector;
performing rod tensor voting on other points with the probability greater than 0 in the neighborhood by taking the characteristic value minimum direction of the points with the probability greater than 0 as a normal direction, and reconstructing the characteristic value and the characteristic vector of each point with the probability greater than 0 according to the voting result to determine the trend direction of the tubular structure of each point with the probability greater than 0;
updating the intensity of each point with the possibility of being greater than 0 in the image by using a diffusion function according to the reconstructed feature vector until the updating times reach the maximum iteration times;
the method comprises the following steps of performing a rod tensor voting on other points with the probability greater than 0 in the neighborhood by taking the characteristic value minimum direction of the point with the probability greater than 0 as a normal direction:
performing rod tensor voting by taking each point with the probability greater than 0 as a voting point, taking the direction with the minimum eigenvalue corresponding to the voting point as a normal direction and taking other points with the probability greater than 0 in the neighborhood as vote number receiving points;
accumulating the ticket numbers Stick (l, theta, pi) received at the ticket number receiving point R, wherein the accumulation process comprises the accumulation of tensor size and direction and the recording of T'R(x, y, z) is an accumulated tensor received by the ticket number receiving point R, and the accumulated tensor is subjected to feature decomposition:
wherein lambda'3，λ′2，λ′1Is T'RCharacteristic value of (x, y, z), and | λ'3|≤|λ′2|≤|λ′1|，Is the accumulated tensor T 'after the voting is finished'R(x, y, z), i.e. the reconstructed eigenvector with the largest eigenvalue λ'1Corresponding feature vectorThe direction of (d) is the diffusion direction.
2. The method for enhancing blood vessels of a pulmonary CT image of claim 1, wherein the step of calculating the Hessian matrix of each point in the image and its eigenvalue and eigenvector and estimating the likelihood that each point belongs to a tubular structure based on the eigenvalue and eigenvector comprises the steps of:
smoothing the image by utilizing a multi-scale Gaussian function;
under each scale, calculating a Hessian matrix of each point in the image according to the smoothing result;
performing eigenvalue decomposition on the Hessian matrix of each point to obtain three eigenvalues and eigenvectors corresponding to the three eigenvalues one by one;
estimating the possibility that each point belongs to the tubular structure under each scale according to the characteristic value and the characteristic vector of each point;
taking the maximum value of the likelihood of each point at different scales as the final value of the likelihood of each point belonging to the tubular structure.
3. The method of claim 2, wherein if the three-dimensional Gaussian function with the scale σ is G (x, y, z; σ), the image is I (x, y, z), and the smoothing result of the image I (x, y, z) at the scale σ is I (x, y, z)σ(x, y, z), the smoothing of the image with the multi-scale gaussian function is represented as:wherein,
if the scale sigma is lower, the Hessian matrix at the point (x, y, z) in the image is Hσ(x, y, z), then the expression of the Hessian matrix for each point in the image is calculated from the smoothing results at each scale as:
<mrow> <msub> <mi>H</mi> <mi>&sigma;</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mfrac> <mrow> <mo>&part;</mo> <msubsup> <mi>I</mi> <mi>&alpha;</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&part;</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mo>&part;</mo> <msubsup> <mi>I</mi> <mi>&alpha;</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&part;</mo> <mi>x</mi> <mo>&part;</mo> <mi>y</mi> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mo>&part;</mo> <msubsup> <mi>I</mi> <mi>&alpha;</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&part;</mo> <mi>x</mi> <mo>&part;</mo> <mi>z</mi> </mrow> </mfrac> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <mo>&part;</mo> <msubsup> <mi>I</mi> <mi>&alpha;</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&part;</mo> <mi>x</mi> <mo>&part;</mo> <mi>y</mi> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mo>&part;</mo> <msubsup> <mi>I</mi> <mi>&alpha;</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&part;</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mo>&part;</mo> <msubsup> <mi>I</mi> <mi>&alpha;</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&part;</mo> <mi>y</mi> <mo>&part;</mo> <mi>z</mi> </mrow> </mfrac> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <mo>&part;</mo> <msubsup> <mi>I</mi> <mi>&alpha;</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&part;</mo> <mi>x</mi> <mo>&part;</mo> <mi>z</mi> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mo>&part;</mo> <msubsup> <mi>I</mi> <mi>&alpha;</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&part;</mo> <mi>y</mi> <mo>&part;</mo> <mi>z</mi> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mrow> <mo>&part;</mo> <msubsup> <mi>I</mi> <mi>&alpha;</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&part;</mo> <msup> <mi>z</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
if the scale sigma is lower, the three characteristic values corresponding to the points (x, y, z) in the image are lambda1、λ2、λ3And satisfy | λ1|≤|λ2|≤|λ3The probability that the point (x, y, z) belongs to a tubular structure is Vs(σ), the estimating the likelihood that each point belongs to the tubular structure at each scale according to the eigenvalue and eigenvector of each point is represented by:
<mrow> <msub> <mi>V</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>&sigma;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msub> <mi>&lambda;</mi> <mn>2</mn> </msub> <mo>></mo> <mn>0</mn> <msub> <mi>or&lambda;</mi> <mn>3</mn> </msub> <mo>></mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msubsup> <mi>R</mi> <mi>A</mi> <mn>2</mn> </msubsup> <mrow> <mn>2</mn> <msup> <mi>&alpha;</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mrow> </msup> <mo>)</mo> <mo>&CenterDot;</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msubsup> <mi>R</mi> <mi>B</mi> <mn>2</mn> </msubsup> <mrow> <mn>2</mn> <msup> <mi>&beta;</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mrow> </msup> <mo>&CenterDot;</mo> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mi>S</mi> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msup> <mi>&gamma;</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mrow> </msup> <mo>)</mo> <mo>&CenterDot;</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <mrow> <mn>2</mn> <msup> <mi>Coeff</mi> <mn>2</mn> </msup> </mrow> <mrow> <mo>|</mo> <msub> <mi>&lambda;</mi> <mn>2</mn> </msub> <mo>|</mo> <msubsup> <mi>&lambda;</mi> <mn>3</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> </mrow> </msup> </mrow> </mtd> <mtd> <mrow> <mi>o</mi> <mi>t</mi> <mi>h</mi> <mi>e</mi> <mi>r</mi> <mi>w</mi> <mi>i</mi> <mi>s</mi> <mi>e</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
wherein,coeff is a constant, α is a constant and 0 < α < 1, β is a constant and 0 < β < 1, γ is a set constant;
taking the maximum value of the possibility of each point under different scales as the final value of the possibility that each point belongs to the tubular structure, and assuming that the final value of the possibility is marked as V, the following steps are performed:wherein σmin，σmaxRespectively, a minimum scale and a maximum scale.
4. The method of claim 1, wherein the three feature values corresponding to the points (x, y, z) with a probability greater than 0 in the image are λ1、λ2、λ3And satisfy | λ1|≤|λ2|≤|λ3Corresponding feature vector isTaking the direction with the minimum characteristic value of the point (x, y, z) as a normal direction, and the point R with the probability greater than 0 in the neighborhood as a vote number receiving point, the point (x, y, z) is in the direction of the normal directionThe number of votes cast by the point R is a Stick tensor Stick (l, θ, π) that includes direction and intensity, and satisfies:
<mrow> <mi>S</mi> <mi>t</mi> <mi>i</mi> <mi>c</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>l</mi> <mo>,</mo> <mi>&theta;</mi> <mo>,</mo> <mi>&pi;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>&lambda;</mi> <mn>3</mn> </msub> <mo>-</mo> <msub> <mi>&lambda;</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mi>D</mi> <mi>F</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>,</mo> <mi>k</mi> <mo>,</mo> <mi>&sigma;</mi> <mo>)</mo> </mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mo>-</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mo>(</mo> <mn>2</mn> <mi>&theta;</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>(</mo> <mn>2</mn> <mi>&theta;</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>&theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>&theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mrow>
wherein,is a significant attenuation function, andtheta is the line l connecting point (x, y, z) and point RThe included angle of the stretched plane, s is the arc length of the connecting line l, sigma designates the voting scale range, determines the size of the voting window, and c is a function of the scale range sigma and meets the following requirements:
5. the method for enhancing blood vessels of a pulmonary CT image of claim 1, wherein the diffusion function isWherein, VtIs the intensity of the vessel after diffusion, t is the diffusion time,is the divergence operator, V is the probability that the point (x, y, z) in the image belongs to a tubular structure, D is the diffusion tensor, and satisfies:
<mrow> <msubsup> <mi>&lambda;</mi> <mn>1</mn> <mrow> <mo>&prime;</mo> <mo>&prime;</mo> </mrow> </msubsup> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msup> <mi>V</mi> <mfrac> <mn>1</mn> <mi>L</mi> </mfrac> </msup> </mrow>
<mrow> <msubsup> <mi>&lambda;</mi> <mn>2</mn> <mrow> <mo>&prime;</mo> <mo>&prime;</mo> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>&lambda;</mi> <mn>3</mn> <mrow> <mo>&prime;</mo> <mo>&prime;</mo> </mrow> </msubsup> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mrow> <mo>(</mo> <mi>&epsiv;</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msup> <mi>V</mi> <mfrac> <mn>1</mn> <mi>L</mi> </mfrac> </msup> </mrow>
wherein,omega is a parameter for the reconstructed feature vector to indicate the strength of anisotropic diffusion; is a parameter to ensure that the diffusion tensor D is a positive definite matrix, ω is greater than; l is a parameter that controls the sensitivity of the diffusion function to the effects of blood vessels.
6. A vessel enhancement system for CT images of the lungs, the system comprising:
the calculation module is used for calculating a Hessian matrix of each point in the image, the eigenvalue and the eigenvector of the Hessian matrix, and estimating the possibility that each point belongs to the tubular structure according to the eigenvalue and the eigenvector;
the reconstruction module is used for carrying out the rod tensor voting on other points with the possibility of being greater than 0 by taking the characteristic value minimum direction of the point with the possibility of being greater than 0 as the normal direction, and reconstructing the characteristic value and the characteristic vector of each point with the possibility of being greater than 0 according to the voting result so as to determine the trend direction of the tubular structure of the point with the possibility of being greater than 0;
the diffusion module is used for updating the intensity of each point with the possibility of being greater than 0 in the image by using a diffusion function according to the reconstructed feature vector until the updating times reach the maximum iteration times;
wherein the reconstruction module comprises:
the voting submodule is used for carrying out the rod tensor voting by taking each point with the possibility of being greater than 0 as a voting point, taking the minimum direction of the characteristic value corresponding to the voting point as the normal direction and taking other points with the possibility of being greater than 0 in the neighborhood as vote number receiving points;
the reconstruction submodule is used for reconstructing the characteristic value and the characteristic vector of each point with the probability greater than 0 according to the voting result so as to determine the trend direction of the tubular structure of each point with the probability greater than 0;
accumulating the ticket numbers Stick (l, theta, pi) received at the ticket number receiving point R, wherein the accumulation process comprises the accumulation of tensor size and direction and the recording of T'R(x, y, z) is an accumulated tensor received by the ticket number receiving point R, and the accumulated tensor is subjected to feature decomposition:
wherein lambda'3，λ′2，λ′1Is T'RCharacteristic value of (x, y, z), and | λ'3|≤|λ′2|≤|λ′1|，Is the accumulated tensor T 'after the voting is finished'R(x, y, z), i.e. the reconstructed eigenvector with the largest eigenvalue λ'1Corresponding feature vectorThe direction is the diffusion direction.
7. The pulmonary CT image vessel enhancement system of claim 6, wherein the calculation module comprises:
the smoothing submodule is used for smoothing the image by utilizing a multi-scale Gaussian function;
the first calculation submodule is used for calculating a Hessian matrix of each point in the image according to the smoothing result under each scale;
the second calculation submodule is used for carrying out eigenvalue decomposition on the Hessian matrix of each point to obtain three eigenvalues and eigenvectors corresponding to the three eigenvalues one by one;
the estimation submodule is used for estimating the possibility that each point belongs to the tubular structure under each scale according to the characteristic value and the characteristic vector of each point;
and the value sub-module is used for taking the maximum value of the possibility of each point under different scales as the final value of the possibility that each point belongs to the tubular structure.
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